Prove: If y>0 then there exists a natural number, n, such that n-1 is less than or equal to y < n.

I'm supposed to prove using the well-ordering property on the set {m as an element of the natural numbers : m > y}

October 15th 2008, 08:13 AM

Plato

Quote:

Originally Posted by GoldendoodleMom

Prove: If y>0 then there exists a natural number, n, such that n-1 is less than or equal to y < n.
I'm supposed to prove using the well-ordering property on the set {m as an element of the natural numbers : m > y}

To use that, you must know that is not bounded above.
Because that is true, .
Every nonempty subset of has a first term.
Let
Moreover, because .